The minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO is characterized up to logarithmic factors, with a polynomial-time algorithm based on Lipschitz extensions of the empirical loss and a nearly matching lower bound.
Online learning and online convex optimization
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A dynamic pruning reduction from agnostic to realizable online learning via weak-consistency oracles achieves O(T^{d_VC+1}) query complexity with near-optimal regret and supplies matching upper and lower bounds on the regret-oracle tradeoff.
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Optimal Rates for Pure $\varepsilon$-Differentially Private Stochastic Convex Optimization with Heavy Tails
The minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO is characterized up to logarithmic factors, with a polynomial-time algorithm based on Lipschitz extensions of the empirical loss and a nearly matching lower bound.
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Regret-Oracle Complexity Tradeoffs in Agnostic Online Learning
A dynamic pruning reduction from agnostic to realizable online learning via weak-consistency oracles achieves O(T^{d_VC+1}) query complexity with near-optimal regret and supplies matching upper and lower bounds on the regret-oracle tradeoff.